Answer:
Step-by-step explanation:
![T = \frac{1}{2}m^{2}+2m - 4\\\\T = 2m + 4\\\\\frac{1}{2}m^{2}+2m - 4 = 2m + 4\\\\\frac{1}{2}m^{2}+2m - 4 - 2m - 4 = 0](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%2B2m%20-%204%5C%5C%5C%5CT%20%3D%202m%20%2B%204%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%2B2m%20-%204%20%3D%202m%20%2B%204%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%2B2m%20-%204%20-%202m%20-%204%20%3D%200)
Combine like terms
![\frac{1}{2}m^{2}+2m - 2m - 4 - 4 = 0\\\\\frac{1}{2}m^{2} - 8 = 0\\\\\frac{1}{2}m^{2} =8\\\\m^{2} = 8*2\\\\m^{2} = 16\\\\m = \sqrt{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%2B2m%20-%202m%20-%204%20-%204%20%3D%200%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%20-%208%20%3D%200%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dm%5E%7B2%7D%20%3D8%5C%5C%5C%5Cm%5E%7B2%7D%20%3D%208%2A2%5C%5C%5C%5Cm%5E%7B2%7D%20%3D%2016%5C%5C%5C%5Cm%20%3D%20%5Csqrt%7B16%7D)
m = ± 4
Answer:
Hey! The answer is <em>-4 5/12</em>
Step-by-step explanation:
<em>First, make all the mixed number into a improper fraction.</em>
<em>Next, find the least common multiple.</em>
<em>Than, adjust the fractions basied on the LCM.</em>
<em>Lastly, convert the improper fractions to mixed numbers</em>
<em>follow these steps in order to get -4 5/12 as your answer.</em>
<em>so therefore your answer will be:</em>
<em>-4 5/12</em>
hope this helps!
Answer:
15 cakes can be decorated.
Step-by-step explanation:
Given:
Total number of shapes Liu has = 140
Ratio of shape of stars and hearts = 4 : 3
According to the question:
Each cake have 5 stars and 4 hearts.
Let the number of starts be "4x" and number of hearts be "3x" from the ratio.
Now,
⇒ ![4x+3x=140](https://tex.z-dn.net/?f=4x%2B3x%3D140)
⇒ ![7x=140](https://tex.z-dn.net/?f=7x%3D140)
⇒ ![x=\frac{140}{7}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B140%7D%7B7%7D)
⇒ ![x=20](https://tex.z-dn.net/?f=x%3D20)
Number of stars = ![4x =4(20) =80](https://tex.z-dn.net/?f=4x%20%3D4%2820%29%20%3D80)
Number of hearts = ![3x=3(20)=60](https://tex.z-dn.net/?f=3x%3D3%2820%29%3D60)
Each cake have 5 stars and 4 hearts .
How many cakes can be decorated with 80 stars.
⇒ No.of cakes = Total number of stars / 5
⇒ ![C=\frac{80}{5}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B80%7D%7B5%7D)
⇒ ![C=16](https://tex.z-dn.net/?f=C%3D16)
How many cakes can be decorated with 60 hearts.
⇒ ![C=\frac{60}{4}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B60%7D%7B4%7D)
⇒ ![C=15](https://tex.z-dn.net/?f=C%3D15)
But both shapes are in combination so only 15 cakes can be decorated with the combination of 5 stars and 4 hearts.
Liu can decorate 15 cakes and only.
Answer:
1/35
Step-by-step explanation:
Number of students born in a country other than the United States = 1/20
Also, 4/7 of 1/20 were born in Puerto Rico
Portion of the student body born in Puerto Rico is therefore = 4/7 of 1/20
4/7 x 1/20
Multiply through
4/140
1/35
W- (3,4)
Z- (-1,1)
X-(-1,-3)
Y-(-4,1)